HETEROCLINIC ORBITS, MOBILITY PARAMETERS AND STABILITY FOR THIN FILM TYPE EQUATIONS
Bibliographic record
Abstract
. We study numerically the phase space of the evolution equation h t = (h n h xxx ) x B(h m h x ) x : Here h(x; t) 0, n > 0 and m 2 R, and the Bond number B is positive. We pursue three goals: to investigate the nonlinear stability of the positive periodic and constant steady states; to locate heteroclinic connecting orbits between these steady states and the compactly supported `droplet' steady states; and to determine how these orbits change when the `mobility' exponents n and m are changed. For example, when n + 1 m < n + 2 we know from the companion article that there can be three fundamentally dierent steady states with the same period and volume. The rst is a constant steady state that is a local minimum of the energy. The second is a positive periodic steady state that is a saddle for the energy and has higher energy than the constant steady state. The third is a periodic collection of droplet steady states having lower energy than either the positive or co...
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.001 | 0.000 |
| Insufficient payload (model declined to judge) | 0.003 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".